Taking the example in this comment thread, even if the model takes an arbitrary nonparametric distribution of input temperatures and perfectly returns the posterior distribution of freezing events there is still a difference in model error and forward UQ error.
The model itself can perfectly describe the physics, but it only knows what you can give it. This may be limited by measurement uncertainty of your equipment, etc, but it is separate from the model itself.
In this area, "the model" is typically considered as the input parameter to quantity of interest map itself. It's not the full problem from gathering data to prediction.
Model error would be things like failing to capture the physics (due to approximations, compute limits, etc), intrinsic aleatoric uncertainty in the freezing process itself, etc.
Making this distinction helps talk about where the uncertainty comes from, how it can be mitigated, and how to use higher level models and resampling to understand its impact across the full problem.
The model itself can perfectly describe the physics, but it only knows what you can give it. This may be limited by measurement uncertainty of your equipment, etc, but it is separate from the model itself.
In this area, "the model" is typically considered as the input parameter to quantity of interest map itself. It's not the full problem from gathering data to prediction.
Model error would be things like failing to capture the physics (due to approximations, compute limits, etc), intrinsic aleatoric uncertainty in the freezing process itself, etc.
Making this distinction helps talk about where the uncertainty comes from, how it can be mitigated, and how to use higher level models and resampling to understand its impact across the full problem.